If the rotation of the shaft were uniform and there were no lost motion in the shaft or connecting-rod, this diagonal line would repeat itself precisely, and would be a straight line modified by the angular vibration of the connecting-rod. On the other hand, these lost motions and the variations in the rotative speed must be exactly recorded, the latter being exhibited with a degree of accuracy not attainable by computation and plotting, and their correctness would be self-demonstrated. For this purpose this instrument must be found highly valuable, if it is really desired to have these variations revealed rather than concealed. Fig. 5 represents the inertia diagram drawn by this instrument applied to a Porter-Allen engine running in the Boston Post Office at the speed of 265 revolutions per minute. Fig. 4 shows the same diagram with the transverse motion of the pencil enlarged to correspond with the scale of the indicator, so exhibiting the force actually exerted on the crank-pin at every point, which is represented by the shaded area, and from which the rotative effect on the crank can be computed. The steam pressure absorbed at the commencement of the stroke by the inertia of these parts is represented by the blank area above the atmospheric line _xx_. This is not all imparted to the crank at the end on account of the compression. I have myself had no experience in the use of this instrument, but I do not see why it might not be so made that the diagonal line or lines in Fig. 4 would be drawn at once. The variations of motion would thus be shown much more accurately than they can be by the enlargement of these small indications. This would require the spring _e_ to bear the same relation to the inertia of the weight _h_ that the spring of the indicator bears to the steam pressure on its piston area. The steam diagram and the inertia diagram would then be drawn to the same scale. A separate instrument would be required for each scale. It would seem desirable that this instrument, which is not expensive, should be brought before the public in this practical shape. The 16″×30″ engine exhibited at this fair of the American Institute was sold from the exhibition to the Arlington Mills, at Lawrence, Mass. For a reason that will appear later, I have always regarded this sale as the most important one that I ever made. CHAPTER XIX Boiler Tests in Exhibition of 1871. We Lose Mr. Allen. Importance of Having a Business Man as President. Devotion of Mr. Hope.